LMAXFOCK

LMAXFOCK = [integer]
Default: LMAXFOCK = 4 

Description: LMAXFOCK sets the maximum angular momentum quantum number l for the augmentation of charge densities in Hartree-Fock type routines.

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In the PAW method, the difference between the charge density of the all-electron partial waves $\phi _{\beta }$ and the pseudo partial waves ${\tilde {\phi }}_{\beta }$ $Q_{\alpha \beta }(r)=\phi _{\alpha }^{*}(r)\phi _{\beta }(r)-{\tilde {\phi }}_{\alpha }^{*}(r){\tilde {\phi }}_{\beta }(r)$ is usually restored on spherical grids centered at each atom (one-center terms inside the PAW spheres). To describe long range electrostatic effect, the moments of the differences of the all-electron and pseudo charge density also need to added on the plane wave grid. This is done up to a certain l quantum number. These augmentation charges exactly restore the moments of the all-electron density on the plane wave grid. For the charge densities used in the Hartree and DFT term, the augmentation is done exactly up to the maximum l quantum number required by the POTCAR files, whereas for the Fock exchange, the augmentation on the plane wave grid is controlled by LMAXFOCK.

Specifically, when the exchange energy is evaluated

$E_{\mathrm {x} }=-{\frac {e^{2}}{2}}\sum _{\mathbf {k} n,\mathbf {q} m}f_{\mathbf {k} n}f_{\mathbf {q} m}\times \int \int d^{3}\mathbf {r} d^{3}\mathbf {r} '{\frac {\psi _{\mathbf {k} n}^{*}(\mathbf {r} )\psi _{\mathbf {q} m}^{*}(\mathbf {r} ')\psi _{\mathbf {k} n}(\mathbf {r} ')\psi _{\mathbf {q} m}(\mathbf {r} )}{\vert \mathbf {r} -\mathbf {r} '\vert }}$

the overlap density $\psi _{\mathbf {k} n}^{*}(\mathbf {r} )\psi _{\mathbf {q} m}(\mathbf {r} )$ between two Bloch orbitals needs to be calculated on the plane wave grid. The tag LMAXFOCK controls up to which l quantum number, augmentation charges are added on the plane wave grid. To accelerate convergence with respect to LMAXFOCK, VASP uses a small trick: the contributions from the Hartree-Fock one-center terms are evaluated for the pseudo orbitals also only up to l=LMAXFOCK, whereas the one-center terms for the exact all-electron orbitals are evaluated up to the maximum required l (twice the angular quantum number of the partial wave with the highest l). The default is LMAXFOCK=4, and it might be necessary to increase this parameter, if the system contains f-electrons. Since this increases the computational load considerably (factor 2), it is recommended to perform tests, whether the results are already reasonably converged using the default LMAXFOCK=4.

To be compatible w.r.t. old releases, VASP also reads the flag HFLMAX to the same effect as LMAXFOCK.

Related Tags and Sections

HFLMAX, LMAXFOCKAE

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